336 lines
13 KiB
C++
336 lines
13 KiB
C++
/*
|
|
* Copyright 2017 The WebRTC Project Authors. All rights reserved.
|
|
*
|
|
* Use of this source code is governed by a BSD-style license
|
|
* that can be found in the LICENSE file in the root of the source
|
|
* tree. An additional intellectual property rights grant can be found
|
|
* in the file PATENTS. All contributing project authors may
|
|
* be found in the AUTHORS file in the root of the source tree.
|
|
*/
|
|
|
|
// Minimum and maximum
|
|
// ===================
|
|
//
|
|
// rtc::SafeMin(x, y)
|
|
// rtc::SafeMax(x, y)
|
|
//
|
|
// (These are both constexpr.)
|
|
//
|
|
// Accept two arguments of either any two integral or any two floating-point
|
|
// types, and return the smaller and larger value, respectively, with no
|
|
// truncation or wrap-around. If only one of the input types is statically
|
|
// guaranteed to be able to represent the result, the return type is that type;
|
|
// if either one would do, the result type is the smaller type. (One of these
|
|
// two cases always applies.)
|
|
//
|
|
// * The case with one floating-point and one integral type is not allowed,
|
|
// because the floating-point type will have greater range, but may not
|
|
// have sufficient precision to represent the integer value exactly.)
|
|
//
|
|
// Clamp (a.k.a. constrain to a given interval)
|
|
// ============================================
|
|
//
|
|
// rtc::SafeClamp(x, a, b)
|
|
//
|
|
// Accepts three arguments of any mix of integral types or any mix of
|
|
// floating-point types, and returns the value in the closed interval [a, b]
|
|
// that is closest to x (that is, if x < a it returns a; if x > b it returns b;
|
|
// and if a <= x <= b it returns x). As for SafeMin() and SafeMax(), there is
|
|
// no truncation or wrap-around. The result type
|
|
//
|
|
// 1. is statically guaranteed to be able to represent the result;
|
|
//
|
|
// 2. is no larger than the largest of the three argument types; and
|
|
//
|
|
// 3. has the same signedness as the type of the third argument, if this is
|
|
// possible without violating the First or Second Law.
|
|
//
|
|
// There is always at least one type that meets criteria 1 and 2. If more than
|
|
// one type meets these criteria equally well, the result type is one of the
|
|
// types that is smallest. Note that unlike SafeMin() and SafeMax(),
|
|
// SafeClamp() will sometimes pick a return type that isn't the type of any of
|
|
// its arguments.
|
|
//
|
|
// * In this context, a type A is smaller than a type B if it has a smaller
|
|
// range; that is, if A::max() - A::min() < B::max() - B::min(). For
|
|
// example, int8_t < int16_t == uint16_t < int32_t, and all integral types
|
|
// are smaller than all floating-point types.)
|
|
//
|
|
// * As for SafeMin and SafeMax, mixing integer and floating-point arguments
|
|
// is not allowed, because floating-point types have greater range than
|
|
// integer types, but do not have sufficient precision to represent the
|
|
// values of most integer types exactly.
|
|
//
|
|
// Requesting a specific return type
|
|
// =================================
|
|
//
|
|
// All three functions allow callers to explicitly specify the return type as a
|
|
// template parameter, overriding the default return type. E.g.
|
|
//
|
|
// rtc::SafeMin<int>(x, y) // returns an int
|
|
//
|
|
// If the requested type is statically guaranteed to be able to represent the
|
|
// result, then everything's fine, and the return type is as requested. But if
|
|
// the requested type is too small, a static_assert is triggered.
|
|
|
|
#ifndef RTC_BASE_NUMERICS_SAFE_MINMAX_H_
|
|
#define RTC_BASE_NUMERICS_SAFE_MINMAX_H_
|
|
|
|
#include <limits>
|
|
#include <type_traits>
|
|
|
|
#include "rtc_base/checks.h"
|
|
#include "rtc_base/numerics/safe_compare.h"
|
|
#include "rtc_base/type_traits.h"
|
|
|
|
namespace rtc {
|
|
|
|
namespace safe_minmax_impl {
|
|
|
|
// Make the range of a type available via something other than a constexpr
|
|
// function, to work around MSVC limitations. See
|
|
// https://blogs.msdn.microsoft.com/vcblog/2015/12/02/partial-support-for-expression-sfinae-in-vs-2015-update-1/
|
|
template <typename T>
|
|
struct Limits {
|
|
static constexpr T lowest = std::numeric_limits<T>::lowest();
|
|
static constexpr T max = std::numeric_limits<T>::max();
|
|
};
|
|
|
|
template <typename T, bool is_enum = std::is_enum<T>::value>
|
|
struct UnderlyingType;
|
|
|
|
template <typename T>
|
|
struct UnderlyingType<T, false> {
|
|
using type = T;
|
|
};
|
|
|
|
template <typename T>
|
|
struct UnderlyingType<T, true> {
|
|
using type = typename std::underlying_type<T>::type;
|
|
};
|
|
|
|
// Given two types T1 and T2, find types that can hold the smallest (in
|
|
// ::min_t) and the largest (in ::max_t) of the two values.
|
|
template <typename T1,
|
|
typename T2,
|
|
bool int1 = IsIntlike<T1>::value,
|
|
bool int2 = IsIntlike<T2>::value>
|
|
struct MType {
|
|
static_assert(int1 == int2,
|
|
"You may not mix integral and floating-point arguments");
|
|
};
|
|
|
|
// Specialization for when neither type is integral (and therefore presumably
|
|
// floating-point).
|
|
template <typename T1, typename T2>
|
|
struct MType<T1, T2, false, false> {
|
|
using min_t = typename std::common_type<T1, T2>::type;
|
|
static_assert(std::is_same<min_t, T1>::value ||
|
|
std::is_same<min_t, T2>::value,
|
|
"");
|
|
|
|
using max_t = typename std::common_type<T1, T2>::type;
|
|
static_assert(std::is_same<max_t, T1>::value ||
|
|
std::is_same<max_t, T2>::value,
|
|
"");
|
|
};
|
|
|
|
// Specialization for when both types are integral.
|
|
template <typename T1, typename T2>
|
|
struct MType<T1, T2, true, true> {
|
|
// The type with the lowest minimum value. In case of a tie, the type with
|
|
// the lowest maximum value. In case that too is a tie, the types have the
|
|
// same range, and we arbitrarily pick T1.
|
|
using min_t = typename std::conditional<
|
|
SafeLt(Limits<T1>::lowest, Limits<T2>::lowest),
|
|
T1,
|
|
typename std::conditional<
|
|
SafeGt(Limits<T1>::lowest, Limits<T2>::lowest),
|
|
T2,
|
|
typename std::conditional<SafeLe(Limits<T1>::max, Limits<T2>::max),
|
|
T1,
|
|
T2>::type>::type>::type;
|
|
static_assert(std::is_same<min_t, T1>::value ||
|
|
std::is_same<min_t, T2>::value,
|
|
"");
|
|
|
|
// The type with the highest maximum value. In case of a tie, the types have
|
|
// the same range (because in C++, integer types with the same maximum also
|
|
// have the same minimum).
|
|
static_assert(SafeNe(Limits<T1>::max, Limits<T2>::max) ||
|
|
SafeEq(Limits<T1>::lowest, Limits<T2>::lowest),
|
|
"integer types with the same max should have the same min");
|
|
using max_t = typename std::
|
|
conditional<SafeGe(Limits<T1>::max, Limits<T2>::max), T1, T2>::type;
|
|
static_assert(std::is_same<max_t, T1>::value ||
|
|
std::is_same<max_t, T2>::value,
|
|
"");
|
|
};
|
|
|
|
// A dummy type that we pass around at compile time but never actually use.
|
|
// Declared but not defined.
|
|
struct DefaultType;
|
|
|
|
// ::type is A, except we fall back to B if A is DefaultType. We static_assert
|
|
// that the chosen type can hold all values that B can hold.
|
|
template <typename A, typename B>
|
|
struct TypeOr {
|
|
using type = typename std::
|
|
conditional<std::is_same<A, DefaultType>::value, B, A>::type;
|
|
static_assert(SafeLe(Limits<type>::lowest, Limits<B>::lowest) &&
|
|
SafeGe(Limits<type>::max, Limits<B>::max),
|
|
"The specified type isn't large enough");
|
|
static_assert(IsIntlike<type>::value == IsIntlike<B>::value &&
|
|
std::is_floating_point<type>::value ==
|
|
std::is_floating_point<type>::value,
|
|
"float<->int conversions not allowed");
|
|
};
|
|
|
|
} // namespace safe_minmax_impl
|
|
|
|
template <
|
|
typename R = safe_minmax_impl::DefaultType,
|
|
typename T1 = safe_minmax_impl::DefaultType,
|
|
typename T2 = safe_minmax_impl::DefaultType,
|
|
typename R2 = typename safe_minmax_impl::TypeOr<
|
|
R,
|
|
typename safe_minmax_impl::MType<
|
|
typename safe_minmax_impl::UnderlyingType<T1>::type,
|
|
typename safe_minmax_impl::UnderlyingType<T2>::type>::min_t>::type>
|
|
constexpr R2 SafeMin(T1 a, T2 b) {
|
|
static_assert(IsIntlike<T1>::value || std::is_floating_point<T1>::value,
|
|
"The first argument must be integral or floating-point");
|
|
static_assert(IsIntlike<T2>::value || std::is_floating_point<T2>::value,
|
|
"The second argument must be integral or floating-point");
|
|
return SafeLt(a, b) ? static_cast<R2>(a) : static_cast<R2>(b);
|
|
}
|
|
|
|
template <
|
|
typename R = safe_minmax_impl::DefaultType,
|
|
typename T1 = safe_minmax_impl::DefaultType,
|
|
typename T2 = safe_minmax_impl::DefaultType,
|
|
typename R2 = typename safe_minmax_impl::TypeOr<
|
|
R,
|
|
typename safe_minmax_impl::MType<
|
|
typename safe_minmax_impl::UnderlyingType<T1>::type,
|
|
typename safe_minmax_impl::UnderlyingType<T2>::type>::max_t>::type>
|
|
constexpr R2 SafeMax(T1 a, T2 b) {
|
|
static_assert(IsIntlike<T1>::value || std::is_floating_point<T1>::value,
|
|
"The first argument must be integral or floating-point");
|
|
static_assert(IsIntlike<T2>::value || std::is_floating_point<T2>::value,
|
|
"The second argument must be integral or floating-point");
|
|
return SafeGt(a, b) ? static_cast<R2>(a) : static_cast<R2>(b);
|
|
}
|
|
|
|
namespace safe_minmax_impl {
|
|
|
|
// Given three types T, L, and H, let ::type be a suitable return value for
|
|
// SafeClamp(T, L, H). See the docs at the top of this file for details.
|
|
template <typename T,
|
|
typename L,
|
|
typename H,
|
|
bool int1 = IsIntlike<T>::value,
|
|
bool int2 = IsIntlike<L>::value,
|
|
bool int3 = IsIntlike<H>::value>
|
|
struct ClampType {
|
|
static_assert(int1 == int2 && int1 == int3,
|
|
"You may not mix integral and floating-point arguments");
|
|
};
|
|
|
|
// Specialization for when all three types are floating-point.
|
|
template <typename T, typename L, typename H>
|
|
struct ClampType<T, L, H, false, false, false> {
|
|
using type = typename std::common_type<T, L, H>::type;
|
|
};
|
|
|
|
// Specialization for when all three types are integral.
|
|
template <typename T, typename L, typename H>
|
|
struct ClampType<T, L, H, true, true, true> {
|
|
private:
|
|
// Range of the return value. The return type must be able to represent this
|
|
// full range.
|
|
static constexpr auto r_min =
|
|
SafeMax(Limits<L>::lowest, SafeMin(Limits<H>::lowest, Limits<T>::lowest));
|
|
static constexpr auto r_max =
|
|
SafeMin(Limits<H>::max, SafeMax(Limits<L>::max, Limits<T>::max));
|
|
|
|
// Is the given type an acceptable return type? (That is, can it represent
|
|
// all possible return values, and is it no larger than the largest of the
|
|
// input types?)
|
|
template <typename A>
|
|
struct AcceptableType {
|
|
private:
|
|
static constexpr bool not_too_large = sizeof(A) <= sizeof(L) ||
|
|
sizeof(A) <= sizeof(H) ||
|
|
sizeof(A) <= sizeof(T);
|
|
static constexpr bool range_contained =
|
|
SafeLe(Limits<A>::lowest, r_min) && SafeLe(r_max, Limits<A>::max);
|
|
|
|
public:
|
|
static constexpr bool value = not_too_large && range_contained;
|
|
};
|
|
|
|
using best_signed_type = typename std::conditional<
|
|
AcceptableType<int8_t>::value,
|
|
int8_t,
|
|
typename std::conditional<
|
|
AcceptableType<int16_t>::value,
|
|
int16_t,
|
|
typename std::conditional<AcceptableType<int32_t>::value,
|
|
int32_t,
|
|
int64_t>::type>::type>::type;
|
|
|
|
using best_unsigned_type = typename std::conditional<
|
|
AcceptableType<uint8_t>::value,
|
|
uint8_t,
|
|
typename std::conditional<
|
|
AcceptableType<uint16_t>::value,
|
|
uint16_t,
|
|
typename std::conditional<AcceptableType<uint32_t>::value,
|
|
uint32_t,
|
|
uint64_t>::type>::type>::type;
|
|
|
|
public:
|
|
// Pick the best type, preferring the same signedness as T but falling back
|
|
// to the other one if necessary.
|
|
using type = typename std::conditional<
|
|
std::is_signed<T>::value,
|
|
typename std::conditional<AcceptableType<best_signed_type>::value,
|
|
best_signed_type,
|
|
best_unsigned_type>::type,
|
|
typename std::conditional<AcceptableType<best_unsigned_type>::value,
|
|
best_unsigned_type,
|
|
best_signed_type>::type>::type;
|
|
static_assert(AcceptableType<type>::value, "");
|
|
};
|
|
|
|
} // namespace safe_minmax_impl
|
|
|
|
template <
|
|
typename R = safe_minmax_impl::DefaultType,
|
|
typename T = safe_minmax_impl::DefaultType,
|
|
typename L = safe_minmax_impl::DefaultType,
|
|
typename H = safe_minmax_impl::DefaultType,
|
|
typename R2 = typename safe_minmax_impl::TypeOr<
|
|
R,
|
|
typename safe_minmax_impl::ClampType<
|
|
typename safe_minmax_impl::UnderlyingType<T>::type,
|
|
typename safe_minmax_impl::UnderlyingType<L>::type,
|
|
typename safe_minmax_impl::UnderlyingType<H>::type>::type>::type>
|
|
R2 SafeClamp(T x, L min, H max) {
|
|
static_assert(IsIntlike<H>::value || std::is_floating_point<H>::value,
|
|
"The first argument must be integral or floating-point");
|
|
static_assert(IsIntlike<T>::value || std::is_floating_point<T>::value,
|
|
"The second argument must be integral or floating-point");
|
|
static_assert(IsIntlike<L>::value || std::is_floating_point<L>::value,
|
|
"The third argument must be integral or floating-point");
|
|
RTC_DCHECK_LE(min, max);
|
|
return SafeLe(x, min)
|
|
? static_cast<R2>(min)
|
|
: SafeGe(x, max) ? static_cast<R2>(max) : static_cast<R2>(x);
|
|
}
|
|
|
|
} // namespace rtc
|
|
|
|
#endif // RTC_BASE_NUMERICS_SAFE_MINMAX_H_
|